No trimming

I’ll first visualize the results broken down across the whole design, followed by a breakdown by only the critical difficulty variable.

dst <- dst %>% 
  mutate(difference = factor(difference, levels = levels(difference)[c(2,1)]),
         selSafeDeck = ifelse(selectedRiskyDeck == 1, 0, 1))

dst %>% 
  group_by(subject, difference, difficulty) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difference, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck) / sqrt(n)) %>% 
  ggplot(aes(x = difficulty, y = ssd, group = difference)) +
  geom_bar(stat = 'identity', aes(fill = difference), color = 'black', position = position_dodge(width = 0.9)) + 
  geom_errorbar(aes(ymin = ssd - se, ymax = ssd + se), position = position_dodge(width = 0.9), width = 0.5) +
  labs(
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Dashed line represents selecting at chance'
  ) +
  ylim(0, 1) +
  geom_hline(yintercept = 0.5, linetype = 'dashed') +
  scale_fill_manual(name = 'Difference', values = c(Moderate = 'light grey', Extreme = 'black')) +
  theme_bw()

Main effect of difficulty:

dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difficulty) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck) / sqrt(n)) %>% 
  ggplot(aes(x = difficulty, y = ssd)) + 
  geom_bar(stat = 'identity') +
  geom_errorbar(aes(ymin = ssd - se, ymax = ssd + se), width = 0.5) +
  labs(
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Dashed line represents selecting at chance'
  ) + 
  ylim(0,1) +
  geom_hline(yintercept = 0.5, linetype = 'dashed') +
  theme_bw()

Visualize subject data underlying the difficulty variable:

uSubjects <- unique(dst$subject)

subjectCode <- data.frame(subject = uSubjects)
subjectCode$subjectLabel <- factor('', levels = c('Supports prospect theory', 'Opposite prospect theory', 'No difference'))

for (i in uSubjects) {
  t <- dst[dst$subject == i, c('difficulty', 'selSafeDeck')]
  mns <- c(e = mean(t[t$difficulty == 'Easier than Reference',]$selSafeDeck), h = mean(t[t$difficulty == 'Harder than Reference',]$selSafeDeck))
  
  
  if (mns[1] != mns[2]) {
    m1 <- t.test(t[t$difficulty == 'Easier than Reference',]$selSafeDeck, t[t$difficulty == 'Harder than Reference',]$selSafeDeck, within = TRUE)
  } else {
    subjectCode[subjectCode$subject == i,]$subjectLabel <- 'No difference'
    next
  }
  
  if (mns['e'] > mns['h'] & m1$p.value < .05) {
    subjectCode[subjectCode$subject == i,]$subjectLabel <- 'Supports prospect theory'
  } else if (mns['e'] < mns['h'] & m1$p.value < .05) {
    subjectCode[subjectCode$subject == i,]$subjectLabel <- 'Opposite prospect theory'
  } else {
    subjectCode[subjectCode$subject == i,]$subjectLabel <- 'No difference'
  }
} 

dst <- subjectCode %>% 
  inner_join(dst)

condMeans <- dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck)) %>% 
  group_by(difficulty) %>% 
  summarize(ssd = mean(ssd))

# dst %>% 
#   group_by(subject, subjectLabel) %>% 
#   summarize(count = n()) %>% 
#   group_by(subjectLabel) %>% 
#   summarize(count = n())

dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck)) %>% 
  ggplot(aes(x = difficulty, y = ssd)) +
  geom_violin(fill = NA, alpha = 0.2) + 
  geom_boxplot(fill = NA, alpha = 0.3) +
  geom_jitter(alpha = 0.4, width = .05, height = 0) +
  geom_line(aes(group = subject), linetype = 'dashed', alpha = .3) +
  geom_point(data = condMeans, aes(x = difficulty, y = ssd), size = 4, shape = 23, color = 'black', fill = 'red') +
  geom_hline(yintercept = 0.5, linetype = 'dotted') +
  geom_label(data = condMeans, aes(x = difficulty, y = ssd, label = round(ssd, 2)), hjust = 1.5, vjust = 1.5) +
  #scale_color_manual(name = 'Subject Label', values = c(`Supports prospect theory` = 'dark green', `Opposite prospect theory` = 'red', `No difference` = 'black')) +
  ylim(0,1) + 
  theme_bw() +
  labs(
    title = 'Selection of safe deck by difficulty and subject',
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Red diamond reflects condition means. Horizontal, black, solid lines reflect medians.'
  ) +
  theme(legend.position = 'bottom')

m1 <- ezANOVA(wid = subject, within = .(difference, difficulty), dv = selSafeDeck, data = dst, detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

m1a <- data.frame(m1$ANOVA)
m1a$p <- round(m1a$p, 3)
m1a$n2p <- round(m1a$SSn / (m1a$SSn + m1a$SSd),3)
m1a

dst %>% 
  group_by(difference, subject) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difference) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck)/ sqrt(n))

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difficulty), dv = selSafeDeck, data = dst[dst$difference == 'Extreme',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difficulty for Extreme difference'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difficulty), dv = selSafeDeck, data = dst[dst$difference == 'Moderate',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difficulty for Moderate difference'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difference), dv = selSafeDeck, data = dst[dst$difficulty == 'Easier than Reference',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difference for easier than reference difficulty'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difference), dv = selSafeDeck, data = dst[dst$difficulty == 'Harder than Reference',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difference for harder than reference difficulty'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

Trial trimming

I’ll first visualize the results broken down across the whole design, followed by a breakdown by only the critical difficulty variable.

dst <- read.csv('../../../data/dstCleanChoice1.csv')
dst <- dst %>% 
  mutate(difference = factor(difference, levels = levels(difference)[c(2,1)]),
         selSafeDeck = ifelse(selectedRiskyDeck == 1, 0, 1))

dst %>% 
  group_by(subject, difference, difficulty) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difference, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck) / sqrt(n)) %>% 
  ggplot(aes(x = difficulty, y = ssd, group = difference)) +
  geom_bar(stat = 'identity', aes(fill = difference), color = 'black', position = position_dodge(width = 0.9)) + 
  geom_errorbar(aes(ymin = ssd - se, ymax = ssd + se), position = position_dodge(width = 0.9), width = 0.5) +
  labs(
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Dashed line represents selecting at chance'
  ) +
  ylim(0, 1) +
  geom_hline(yintercept = 0.5, linetype = 'dashed') +
  scale_fill_manual(name = 'Difference', values = c(Moderate = 'light grey', Extreme = 'black')) +
  theme_bw()

Main effect of difficulty:

dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difficulty) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck) / sqrt(n)) %>% 
  ggplot(aes(x = difficulty, y = ssd)) + 
  geom_bar(stat = 'identity') +
  geom_errorbar(aes(ymin = ssd - se, ymax = ssd + se), width = 0.5) +
  labs(
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Dashed line represents selecting at chance'
  ) + 
  ylim(0,1) +
  geom_hline(yintercept = 0.5, linetype = 'dashed') +
  theme_bw()

Visualize subject data underlying the difficulty variable:

condMeans <- dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck)) %>% 
  group_by(difficulty) %>% 
  summarize(ssd = mean(ssd))

# dst %>% 
#   group_by(subject, subjectLabel) %>% 
#   summarize(count = n()) %>% 
#   group_by(subjectLabel) %>% 
#   summarize(count = n())

dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck)) %>% 
  ggplot(aes(x = difficulty, y = ssd)) +
  geom_violin(fill = NA, alpha = 0.2) + 
  geom_boxplot(fill = NA, alpha = 0.3) +
  geom_jitter(alpha = 0.4, width = .05, height = 0) +
  geom_line(aes(group = subject), linetype = 'dashed', alpha = .3) +
  geom_point(data = condMeans, aes(x = difficulty, y = ssd), size = 4, shape = 23, color = 'black', fill = 'red') +
  geom_hline(yintercept = 0.5, linetype = 'dotted') +
  geom_label(data = condMeans, aes(x = difficulty, y = ssd, label = round(ssd, 2)), hjust = 1.5, vjust = 1.5) +
  scale_color_manual(name = 'Subject Label', values = c(`Supports prospect theory` = 'dark green', `Opposite prospect theory` = 'red', `No difference` = 'black')) +
  ylim(0,1) + 
  theme_bw() +
  labs(
    title = 'Selection of safe deck by difficulty and subject',
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Red diamond reflects condition means. Horizontal, black, solid lines reflect medians.'
  ) +
  theme(legend.position = 'bottom')

m1 <- ezANOVA(wid = subject, within = .(difference, difficulty), dv = selSafeDeck, data = dst, detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

m1a <- data.frame(m1$ANOVA)
m1a$p <- round(m1a$p, 3)
m1a$n2p <- round(m1a$SSn / (m1a$SSn + m1a$SSd),3)
m1a

dst %>% 
  group_by(difference, subject) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difference) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck)/ sqrt(n))

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difficulty), dv = selSafeDeck, data = dst[dst$difference == 'Extreme',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difficulty for Extreme difference'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difficulty), dv = selSafeDeck, data = dst[dst$difference == 'Moderate',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difficulty for Moderate difference'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difference), dv = selSafeDeck, data = dst[dst$difficulty == 'Easier than Reference',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difference for easier than reference difficulty'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difference), dv = selSafeDeck, data = dst[dst$difficulty == 'Harder than Reference',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difference for harder than reference difficulty'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

Choice-based subject trimming

I’ll first visualize the results broken down across the whole design, followed by a breakdown by only the critical difficulty variable.

dst <- read.csv('../../../data/dstCleanChoice2.csv')
dst <- dst %>% 
  mutate(difference = factor(difference, levels = levels(difference)[c(2,1)]),
         selSafeDeck = ifelse(selectedRiskyDeck == 1, 0, 1))

dst %>% 
  group_by(subject, difference, difficulty) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difference, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck) / sqrt(n)) %>% 
  ggplot(aes(x = difficulty, y = ssd, group = difference)) +
  geom_bar(stat = 'identity', aes(fill = difference), color = 'black', position = position_dodge(width = 0.9)) + 
  geom_errorbar(aes(ymin = ssd - se, ymax = ssd + se), position = position_dodge(width = 0.9), width = 0.5) +
  labs(
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Dashed line represents selecting at chance'
  ) +
  ylim(0, 1) +
  geom_hline(yintercept = 0.5, linetype = 'dashed') +
  scale_fill_manual(name = 'Difference', values = c(Moderate = 'light grey', Extreme = 'black')) +
  theme_bw()

Main effect of difficulty:

dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difficulty) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck) / sqrt(n)) %>% 
  ggplot(aes(x = difficulty, y = ssd)) + 
  geom_bar(stat = 'identity') +
  geom_errorbar(aes(ymin = ssd - se, ymax = ssd + se), width = 0.5) +
  labs(
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Dashed line represents selecting at chance'
  ) + 
  ylim(0,1) +
  geom_hline(yintercept = 0.5, linetype = 'dashed') +
  theme_bw()

Visualize subject data underlying the difficulty variable:

uSubjects <- unique(dst$subject)

subjectCode <- data.frame(subject = uSubjects)
subjectCode$subjectLabel <- factor('', levels = c('Supports prospect theory', 'Opposite prospect theory', 'No difference'))

for (i in uSubjects) {
  t <- dst[dst$subject == i, c('difficulty', 'selSafeDeck')]
  mns <- c(e = mean(t[t$difficulty == 'Easier than Reference',]$selSafeDeck), h = mean(t[t$difficulty == 'Harder than Reference',]$selSafeDeck))
  
  
  if (mns[1] != mns[2]) {
    m1 <- t.test(t[t$difficulty == 'Easier than Reference',]$selSafeDeck, t[t$difficulty == 'Harder than Reference',]$selSafeDeck, within = TRUE)
  } else {
    subjectCode[subjectCode$subject == i,]$subjectLabel <- 'No difference'
    next
  }
  
  if (mns['e'] > mns['h'] & m1$p.value < .05) {
    subjectCode[subjectCode$subject == i,]$subjectLabel <- 'Supports prospect theory'
  } else if (mns['e'] < mns['h'] & m1$p.value < .05) {
    subjectCode[subjectCode$subject == i,]$subjectLabel <- 'Opposite prospect theory'
  } else {
    subjectCode[subjectCode$subject == i,]$subjectLabel <- 'No difference'
  }
} 

dst <- subjectCode %>% 
  inner_join(dst)

condMeans <- dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck)) %>% 
  group_by(difficulty) %>% 
  summarize(ssd = mean(ssd))
# 
# dst %>% 
#   group_by(subject, subjectLabel) %>% 
#   summarize(count = n()) %>% 
#   group_by(subjectLabel) %>% 
#   summarize(count = n())

dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck)) %>% 
  ggplot(aes(x = difficulty, y = ssd)) +
  geom_violin(fill = NA, alpha = 0.2) + 
  geom_boxplot(fill = NA, alpha = 0.3) +
  geom_jitter(alpha = 0.4, width = .05, height = 0) +
  geom_line(aes(group = subject), linetype = 'dashed', alpha = .3) +
  geom_point(data = condMeans, aes(x = difficulty, y = ssd), size = 4, shape = 23, color = 'black', fill = 'red') +
  geom_hline(yintercept = 0.5, linetype = 'dotted') +
  geom_label(data = condMeans, aes(x = difficulty, y = ssd, label = round(ssd, 2)), hjust = 1.5, vjust = 1.5) +
  #scale_color_manual(name = 'Subject Label', values = c(`Supports prospect theory` = 'dark green', `Opposite prospect theory` = 'red', `No difference` = 'black')) +
  ylim(0,1) + 
  theme_bw() +
  labs(
    title = 'Selection of safe deck by difficulty and subject',
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Red diamond reflects condition means. Horizontal, black, solid lines reflect medians.'
  ) +
  theme(legend.position = 'bottom')

m1 <- ezANOVA(wid = subject, within = .(difference, difficulty), dv = selSafeDeck, data = dst, detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

m1a <- data.frame(m1$ANOVA)
m1a$p <- round(m1a$p, 3)
m1a$n2p <- round(m1a$SSn / (m1a$SSn + m1a$SSd),3)
m1a

dst %>% 
  group_by(difference, subject) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difference) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck)/ sqrt(n))

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difficulty), dv = selSafeDeck, data = dst[dst$difference == 'Extreme',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difficulty for Extreme difference'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difficulty), dv = selSafeDeck, data = dst[dst$difference == 'Moderate',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difficulty for Moderate difference'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difference), dv = selSafeDeck, data = dst[dst$difficulty == 'Easier than Reference',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difference for easier than reference difficulty'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)

DFd <- m1$ANOVA$DFd[4]
SSd <- m1$ANOVA$SSd[4]
MSe <- SSd / DFd
omnibusParams <- c(DFd = DFd, SSd = SSd, MSe = MSe)

m2 <- ezANOVA(wid = subject, within = .(difference), dv = selSafeDeck, data = dst[dst$difficulty == 'Harder than Reference',], detailed = TRUE)

## Warning: Converting "subject" to factor for ANOVA.

## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.

s <- 'Simple effect of difference for harder than reference difficulty'
r <- formatSimpleEffects(omnibusParams = omnibusParams, model = m2)
data.frame(Contrast = s, Result = r)